Question

One of the students in the introductory statistics class in exercise 7 claims to have tossed her coin 200 times and found only 42% heads. what do you think of this claim? explain.

Answer 1

For 200 flips, the sampling distribution model is Normal with mean(sub p-hat)=p=0.5;
sigma(sub p-hat)=(root)pq/n
=0.0354
Her sample proportion of p-hat=42% = 0.42
which is about 2.26 standard deviations below the expected proportion,
which is unusual, but not extraordinary.
According to the Normal model, we expect sample proportions this low or lower about 1.2% of the time.

Answer 2

When one student have tossed her coin for 200 times, the sampling distribution model used is

Normal with mean(sub p-hat)= p=0.5; sigma(sub p-hat) = (root)pq/n=0.0354

Her trial proportion of p-hat=.42 is about 2.26 standard deviations below the expected proportion, which is unusual, but not surprising.

Based to the Normal model, the expected sample sizes is low or lower about 1.2% of the time.